Xiuming Yao

Fault Detection Filter Design for Markovian Jump Singular Systems With Intermittent Measurements

This paper addresses the problem of fault detection filter design for discrete-time Markovian jump singular systems with intermittent measurements. The measurement transmission from the plant to the fault detection filter is assumed to be imperfect and a stochastic variable is utilized to model the phenomenon of data missing. Our attention is focused on the design of a fault detection filter such that the residual system is stochastically Markovian jump admissible and satisfies some expected performances. A new necessary and sufficient condition for a class of discrete-time Markovian jump singular systems to be stochastically Markovian jump admissible is proposed in the form of strict linear matrix inequalities. Sufficient conditions are established for the existence of the fault detection filter. Finally, a numerical example is provided to demonstrate the usefulness and applicability of the developed theoretical results.

Robust H∞ filtering of Markovian jump stochastic systems with uncertain transition probabilities

This article investigates the problem of robust ℋ∞ filtering for a class of uncertain Markovian stochastic systems. The system under consideration not only contains Itô-type stochastic disturbances and time-varying delays, but also involves uncertainties both in the system matrices and in the mode transition rate matrix. Our aim is to design an ℋ∞ filter such that, for all admissible parameter uncertainties and time-delays, the filtering error system can be guaranteed to be robustly stochastically stable, and achieve a prescribed ℋ∞ disturbance rejection attenuation level. By constructing a proper stochastic Lyapunov–Krasovskii functional and employing the free-weighting matrix technique, sufficient conditions for the existence of the desired filters are established in terms of linear matrix inequalities, which can be readily solved by standard numerical software. Finally, a numerical example is provided to show the utility of the developed approaches.

Filtering and Control of Stochastic Jump Hybrid Systems

This book presents recent research work on stochastic jump hybrid systems. Specifically, the considered stochastic jump hybrid systems include Markovian jump Ito stochastic systems, Markovian jump linear-parameter-varying (LPV) systems, Markovian jump singular systems, Markovian jump two-dimensional (2-D) systems, and Markovian jump repeated scalar nonlinear systems. Some sufficient conditions are first established respectively for the stability and performances of those kinds of stochastic jump hybrid systems in terms of solution of linear matrix inequalities (LMIs). Based on the derived analysis conditions, the filtering and control problems are addressed. The book presents up-to-date research developments and novel methodologies on stochastic jump hybrid systems. The contents can be divided into two parts: the first part is focused on robust filter design problem, while the second part is put the emphasis on robust control problem. These methodologies provide a framework for stability and performance analysis, robust controller design, and robust filter design for the considered systems. Solutions to the design problems are presented in terms of LMIs. The book is a timely reflection of the developing area of filtering and control theories for Markovian jump hybrid systems with various kinds of imperfect information. It is a collection of a series of latest research results and therefore serves as a useful textbook for senior and/or graduate students who are interested in knowing 1) the state-of-the-art of linear filtering and control areas, and 2) recent advances in stochastic jump hybrid systems. The readers will also benefit from some new concepts, new models and new methodologies with practical significance in control engineering and signal processing

Conclusion and Further Work

This chapter summarizes the results of the book and then proposes some related topics for the future research work.

Fault Detection Filter Design for Markovian Jump Singular Systems

This chapter investigates the fault detection filter design problem for discrete-time Markovian jump singular systems with intermittent measurements. The data missing phenomena is modeled by a Bernoulli distributed stochastic variable. With the introduction of new definitions of stochastic Markovian jump stability and stochastic admissibility for such systems, a new necessary and sufficient condition for Markovian jump singular systems to be stochastically admissible is derived in terms of strict linear matrix inequalities (LMIs). Subsequently, the existence of the \(\mathcal {H}_{\infty }\) fault detection filter such that the residual system is stochastically admissible and meets certain performance requirements is solved. Moreover, the explicit expression of the desired filter parameters is also provided. It is shown that the desired \(\mathcal {H}_{\infty }\) fault detection filter can be obtained by solving a convex optimization problem readily with standard numerical software.

Filter design for discrete-time Markovian jump singular systems with its application to fault detection

This paper is concerned with the problem of fault detection for discrete-time Markovian jump singular systems with intermittent measurements. The measurements transmission from the plant to the fault detection filter is assumed to be imperfect and a stochastic variable is utilized to model the phenomenon of data missing. Our attention is focused on the design of a fault detection filter such that the residual system is stochastic Markovian jump admissible and satisfies some scheduled performance. A new necessary and sufficient condition for a class of discrete-time Markovian jump singular systems to be stochastic Markovian jump admissible is proposed in the form of strict linear matrix inequalities (LMIs). Sufficient conditions are proposed for the existence of fault detection filter. Finally, a numerical example is provided to illustrate the usefulness and applicability of the developed theoretical results.

Quantized Filtering of Markovian Jump LPV Systems

This chapter studies the quantized \(\mathcal {H}_{\infty }\) filtering problem for discrete time Markovian jump linear parameter-varying (LPV) systems subject to intermittent measurements. A logarithmic mode-independent quantizer is employed to quantize the measured output of the underlying plant and a Bernoulli distributed stochastic variable is utilized to model the data missing phenomena. By using the parameter dependent Lyapunov functional method, a sufficient parameterized linear matrix inequality (PLMI) type condition is proposed for the filtering error system. The basic functions and gridding technique are utilized to solve the corresponding parameterized convex problem. Moreover, the explicit expressions of the desired filter parameters are also established.

Output Feedback Control of Markovian Jump Systems with Multiple Disturbances

This chapter is concerned with the problem of the composite DOB output feedback control and passive control for Markovian jump systems with nonlinearity and multiple disturbances. A new CHAD control methodology, which is DOB control plus passive control, for the controlled plant with multiple disturbances is proposed. A new structure of the nonlinear disturbance observer is constructed based on the information of the control input, measurement output and the derivative of the measurement output. DOB output feedback controller is proposed to take place of DOB state feedback controller, which is under the assumption that the system states or the estimation of them are available. To the best of authors’ knowledge, DOB output feedback controller has not been studied yet, due primarily to the mathematical complexities in solving the matrices of the controller. The conditions of the existence of the above controllers are proposed for both MJLs and linear systems with nonlinearity, both of which have not been presented yet, up to now.

Robust Filtering of Markovian Jump Stochastic Systems

This chapter investigates the problem of robust \(\text {H}_\infty \) filtering for a class of uncertain Markovian jump Ito stochastic systems. The system under consideration not only contains Ito-type stochastic disturbances and time-varying delays, but also involves uncertainties both in the system matrices and in the mode transition rate matrix. Our aim is to design an \(\text {H}_\infty \) filter such that, for all admissible parameter uncertainties and time-delays, the filtering error system can be guaranteed to be robustly stochastically stable, and achieve a prescribed \(\text {H}_\infty \) disturbance rejection attenuation level. By constructing a proper stochastic Lyapunov-Krasovskii functional and employing the free-weighting matrix technique, sufficient conditions for the existence of the desired filters are established in terms of LMIs, which can be readily solved by standard numerical software.

Filtering of Markovian Jump 2-D Systems

This chapter considers the \(\mathcal {H}_{\infty }\) filtering problem for Markovian jump 2-D systems. The mathematical model of Markovian jump 2-D systems is established upon the well-known Roesser model. Our attention is focused on the design of a full-order filter, which guarantees the filtering error system to be mean-square asymptotically stable and has a prescribed \(\mathcal {H}_{\infty }\) disturbance attenuation performance. Sufficient conditions for the existence of such filters are established in terms of LMIs, and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved. In addition, the obtained results are further extended to more general cases where the system matrices also contain uncertain parameters. The most frequently used ways of dealing with parameter uncertainties, including polytopic and norm-bounded characterizations, are taken into consideration.